Read the following passage given below and answer the question.

Andehydes and ketones undergo nucleophilic addition reactions. A nucleophile attacks the electrophilic carbon atom of polar carbonyl group from perpendicular to plane of \(sp^2\) hybridized orbitals of carbonyl carbon. The hybridization of carbon changes from \(sp^2\) \(sp^3\) and a tetrahedral alkoxide intermediate is formed. This captures \(H^+\) to give neutral product. In carboxylic acids, carbonyl carbon is less electrophilic than carbonyl carbon carbon of aldehydes and ketones.

An organic compound \(C_3H_6O\) does not give a precipitate with 2,4-finitrophenyl hydrazine and also does not react with metallic sodium. It could be:

\(CH_2=CH-O-CH_3\)

The correct answer is option 4. \(CH_2=CH-O-CH_3\).

Let us break down the reasoning for each option based on the given clues:

Clues: The compound does not give a precipitate with 2,4-dinitrophenylhydrazine. The compound does not react with metallic sodium.

Explanation of Each Option:

1. \( \text{CH}_3\text{CH}_2\text{CHO} \) (Propionaldehyde):

Reaction with 2,4-Dinitrophenylhydrazine: Propionaldehyde is an aldehyde, and aldehydes react with 2,4-dinitrophenylhydrazine to form a yellow or orange precipitate due to the formation of a hydrazone. This means that propionaldehyde should give a precipitate with 2,4-dinitrophenylhydrazine.

Reaction with Metallic Sodium: Propionaldehyde, being an aldehyde, does not react with metallic sodium, as this test is used to detect alcohols with acidic hydrogens.

2. \( \text{CH}_2=\text{CH}-\text{CH}_2\text{OH} \) (3-Hydroxypropene):

Reaction with 2,4-Dinitrophenylhydrazine: This compound does not have a carbonyl group (aldehyde or ketone), so it will not react with 2,4-dinitrophenylhydrazine. Therefore, it correctly fits the clue of not giving a precipitate with this reagent.

Reaction with Metallic Sodium: Although the presence of the hydroxyl group could lead to a reaction with metallic sodium, the reaction is typically more pronounced with alcohols that have more acidic hydrogen atoms (like phenols). The reaction is less pronounced for alcohols adjacent to alkenes. However, the primary reason this compound is correct is due to the first clue.

3. \( \text{CH}_3\text{COCH}_3 \) (Acetone):

Reaction with 2,4-Dinitrophenylhydrazine: Acetone is a ketone and will react with 2,4-dinitrophenylhydrazine to form a yellow or orange precipitate, which means it does not fit the clue of not giving a precipitate.

Reaction with Metallic Sodium: Ketones do not react with metallic sodium, which fits the second clue.

4. \( \text{CH}_2=\text{CH}-\text{O}-\text{CH}_3 \) (Methyl Vinyl Ether):

Reaction with 2,4-Dinitrophenylhydrazine: This compound is an ether and does not have a carbonyl group, so it will not react with 2,4-dinitrophenylhydrazine, correctly fitting the first clue

Reaction with Metallic Sodium: Ethers generally do not react with metallic sodium, which fits the second clue as well.

Summary

Based on the given clues, we need a compound that:

Does not react with 2,4-dinitrophenylhydrazine (indicating the absence of a carbonyl group).

Does not react with metallic sodium (indicating it is not an alcohol with an acidic hydroxyl group).

The only compound that satisfies both conditions is \( \text{CH}_2=\text{CH}-\text{O}-\text{CH}_3 \) (Methyl Vinyl Ether).

This compound fits both clues:

It does not have a carbonyl group, so it won’t react with 2,4-dinitrophenylhydrazine. As an ether, it does not react with metallic sodium.